This invention relates to optical fiber waveguides, and, more particularly, to optical fiber waveguides wherein a central core of optical material is surrounded by a cladding material having a lower index of refraction. This invention also relates to optical fiber waveguides wherein the core-cladding interface has a cross-sectional boundary which is noncircular.
Optical fiber waveguides are now well recognized in the art as desirable mediums for use in the transmission of optical energy. Typically, the optical fiber waveguide consists of a core of optical material having a circular cross section surrounded by a cladding material having a lower index of refraction. If the core is made sufficiently small in diameter relative to the wavelength of light to be transmitted, a single mode of energy is propagated along the core and no dispersion is introduced by virtue of differences in transit time for multiple mode paths within the core. This single mode type of optical fiber is presently impractical however, primarily due to the fact that many of the sources now available for optical transmission systems do not radiate single modes. Instead these sources generate their power into many modes. In addition, the single mode fiber is presently impractical from the standpoint of performing splices of this fiber within the field since the core is so small. Consequently, the multimode fiber has become of much greater practical significance. In the multimode fiber the core diameter is large relative to the wavelength of light being transmitted and the energy is transmitted from transmitting to receiving end by way of several modes that are operative within the fiber.
In the step index fiber wherein the core has a uniform index of refraction, the modes which travel along the axis of the core arrive at the receiving location at a point earlier in time than the modes which transmit by way of multiple reflections from the core-cladding interface. This introduces a dispersion now commonly known in the art as modal dispersion. The first technique for minimizing the effect of modal dispersion was set forth by S. E. Miller in his article entitled "Light Propagation in Generalized Lens-Like Media", Bell System Technical Journal, Vol. 44, 1965, pages 2017-2064. In accordance with this Miller technique, the index of refraction is caused to change along the radial dimension of the fiber core. The index at the core center has the highest value and the index is changed in a roughly parabolic shape so as to decrease to the value of the index in the cladding at the core-cladding interface. This technique assumed that the material dispersion dn.sup.2 /d.lambda. is negligible, where n is the index of refraction and .lambda. is the wavelength of the propagating energy.
It was subsequently discovered that material dispersion cannot be neglected particularly in fibers where the change in the index of refraction is caused to occur by the addition of a substantial amount of additional material known to the art as a dopant. If the added amount of this dopant is low in molar concentration the material dispersion dn.sup.2 /d.lambda. is approximately linear with respect to the square, n.sup.2, of the index of refraction. Under these circumstances, the analysis by Gloge and Marcatili was extended by D. B. Keck and R. Olshansky to cover optical fibers wherein the material dispersion dn.sup.2 /d.lambda. is a linear function of n.sup.2. See for example, their U.S. Pat. No. 3,904,268 entitled "Optical Waveguide Having Optical Index Gradient" issued Sept. 9, 1975. It was determined by Keck and Olshansky that the index profile must still follow a power law shape for minimum modal dispersion but the exponent in the index profile equation was determined to require a value other than the value determined by Miller.
Most recently, it has been discovered by J. A. Arnaud and J. W. Fleming and reported in their article entitled "Pulse Broadening in Multimode Optical Fibers with Large .DELTA.n/n: Numerical Results", Electronics Letters, Apr. 1, 1976, Vol. 12, No. 7, that the material dispersion (dn.sup.2 /d.lambda.) cannot be assumed to be a linear function of the index of refraction squared (n.sup.2) particularly where there are large molar concentrations of dopant that are added to achieve the index profile and also in cases where boron oxide is utilized as a dopant. To achieve minimum modal dispersion in those cases where the material dispersion has an arbitrary dependence on the index of refraction, the index profile can be determined by the inventive technique set forth in the copending application by E. A. J. Marcatili entitled "Optical Fiber Waveguide Having Minimum Modal Dispersion" issued on Nov. 8, 1977 as U.S. Pat. No. 4,057,320. In accordance with this Marcatili invention, the radius r at which each value of the index of refraction n must be located is given in terms of the following equation: ##EQU1## where F is a profile function defined by the equation EQU F = 1 - n.sup.2 /n.sub.o.sup.2,
a is the radius of the core-cladding interface, n.sub.o is the index of refraction on the core axis, d is a constant when the fiber is operated at a single wavelength, p is a profile dispersion parameter determined by measurements on the optical material to be used in the core, and .DELTA. is the relative change of refractive index in the fiber cross-section, ##EQU2## n.sub.c being the index of refraction in the cladding.
As pointed out in the above-identified Marcatili application, his design equations used to obtain minimum modal dispersion are restricted for use with circularly symmetric fibers. Noncircularly symmetric fibers are also of considerable interest in the optical fiber waveguide art. Optical fibers having a noncircularly symmetric profile may prove to be less sensitive to bending losses than fibers with circularly symmetric profiles if bending takes place in one preferred plane. Fibers with noncircularly symmetric profiles would also be easier to couple to the many optical sources that have emitting areas that are shaped in a noncircular fashion. For example, injection lasers and edge-emitting light emitting diodes having large junction widths may be more easily coupled to fibers whose profile is elongated in one direction as compared with fibers having circularly symmetric index profiles.